Shader-based fog without using volumetrics
You can use Ray Length (as suggested by @PGmath) to mix in a 'Fog Shader'.

Use Light Path &gt; Ray Length and Math &gt; Divide to control the spread
Use the result to mix your object's material with a 'Fog Shader'
Add a background plane with the same 'Fog Shader' (so they nicely blend together)

For the 'Fog Shader' set Specular = 0 (to have zero reflectivity)